The constitutive relations developed in the companion paper are used to model detailed observations of preseismic slip and the onset of unstable slip in biaxial laboratory experiments. The simulations employ a deterministic plane strain finite element model to represent the interactions both within the sliding blocks and between the blocks and the loading apparatus. Both experiments and simulations show that preseismic slip is controlled by initial inhomogeneity of shear stress along the sliding surface relative to the frictional strength. As a consequence of the inhomogeneity, stable slip begins at a point on the surface and the area of slip slowly expands as the external loading increases. A previously proposed correlation between accelerating rates of stable slip and growth of the area of slip is supported by the simulations. In the simulations and in the experiments, unstable slip occurs shortly after a propagating slip event traverses the sliding surface and breaks out at the ends of the sample. In the model the breakout of stable slip causes a sudden acceleration of slip rates. Because of velocity dependency of the constitutive relationship for friction, the rapid acceleration of slip causes a decrease in frictional strength. Instability occurs when the frictional strength decreases with displacement at a rate that exceeds the intrinsic unloading characteristics of the sample and test machine. A simple slider-spring model that does not consider preseismic slip appears to approximate the transition adequately from stable sliding to unstable slip as a function of normal stress, machine stiffness, and surface roughness for small samples. However, for large samples and for natural faults the simulations suggest that the simple model may be inaccurate because it does not take into account potentially large preseismic displacements that will alter the friction parameters prior to instability. Copyright ?? 1979 by the American Geophysical Union.
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Modeling of rock friction 2. Simulation of preseismic slip